A hemispherical glass body of radius 10 cm and refractive index 1.5… | JEE Main 2016 (10 Apr, Shift 1)

Q69JEE Main 2016 · 10 APR · SHIFT 1Difficult

Combination of Lenses

A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6 cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen:

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Answer: (c)

Curved surface is a concave mirror: $R = 10$ , $f = 5\text{ cm}$ ; bubble is $10 - 6 = 4\text{ cm}$ from the pole.
$\frac{1}{v} = -\frac{1}{5} + \frac{1}{4} = \frac{1}{20} \Rightarrow v = 20\text{ cm}$ behind the pole, i.e. $30\text{ cm}$ below the flat surface.
Seen through the flat surface: apparent depth $= \frac{30}{1.5} = 20\text{ cm}$
So the answer is (c) 20 cm below flat surface.

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